The Science of Sound

When you pluck a guitar string or blow into a saxophone, the air vibrates at a specific frequency. This frequency is what we perceive as pitch. But here’s the interesting part: that string doesn’t just vibrate at one frequency—it also vibrates at multiples of that frequency called harmonics or overtones.

For example, if you play a note vibrating at 100 Hz (cycles per second), you also get quieter vibrations at 200 Hz, 300 Hz, 400 Hz, and so on. These harmonics are what give each instrument its unique tone color. They’re also the foundation of how we built our musical system.

From Nature to the 12-Note System

Ancient musicians discovered that certain notes sound good together because their harmonics align naturally. The most consonant interval is the octave—a note that vibrates exactly twice as fast as another (like 100 Hz and 200 Hz). Our ears perceive these as essentially “the same note” at different heights.

The next most consonant interval is the perfect fifth (frequency ratio 3:2). If you keep stacking perfect fifths and bringing them back within one octave, you get most of the notes we use in music. This process led different cultures to develop various tuning systems.

Western music eventually settled on the 12-tone equal temperament system. Instead of using pure harmonic ratios (which created tuning problems when changing keys), we divided the octave into 12 equal steps called semitones or half steps. Each semitone is exactly the 12th root of 2 (about 1.05946) times the frequency of the previous note.

This compromise slightly “detuned” the pure harmonic intervals but gave us the freedom to play in any key and modulate between keys smoothly—essential for the rich harmonic language of Western music.

Understanding Intervals

An interval is simply the distance between two notes, measured in semitones:

• Half step (H) = 1 semitone (adjacent notes, like C to C# or E to F)
• Whole step (W) = 2 semitones (like C to D or E to F#)

Here are all the intervals within an octave that you’ll encounter in scales and chords:

• Minor 2nd (♭2) = 1 semitone (H)
• Major 2nd (2) = 2 semitones (W)
• Minor 3rd (♭3) = 3 semitones
• Major 3rd (3) = 4 semitones
• Perfect 4th (4) = 5 semitones
• Augmented 4th / Diminished 5th (#4/♭5) = 6 semitones (tritone)
• Perfect 5th (5) = 7 semitones
• Minor 6th (♭6) = 8 semitones
• Major 6th (6) = 9 semitones
• Minor 7th (♭7) = 10 semitones
• Major 7th (7) = 11 semitones
• Octave (8) = 12 semitones

These intervals are the building blocks of all scales and chords. The quality of an interval (major, minor, perfect, augmented, diminished) determines the character and emotion of the music.

How This Connects to Scales

A scale is a selection of notes from the 12 available semitones, arranged in a specific pattern of whole steps and half steps. Different patterns create different scales with unique sounds and emotional qualities.

Below, you’ll see visual representations where:

• Each row shows all 12 semitones (half-steps) as rectangles numbered 1-12
• These represent the chromatic scale — all 12 possible notes within an octave
• Blackened rectangles show which of these 12 chromatic notes belong to each scale (typically 7 notes)
• White rectangles show the 5 chromatic notes that are NOT in that scale

Important: In this section, the numbers 1-12 represent semitones (chromatic half-steps), not scale degrees. For example, in C: 1=C, 2=C#/Db, 3=D, 4=D#/Eb, 5=E, 6=F, 7=F#/Gb, 8=G, 9=G#/Ab, 10=A, 11=A#/Bb, 12=B.

The modes are different scales that share the same set of notes but start from different positions. This creates different interval patterns and gives each mode its characteristic sound—all derived from the same parent scale.

Think of it this way: the 12 semitones are like a palette of colors, and each scale/mode is a different selection from that palette. The visual grid below makes these selections immediately clear.

Melodic Minor Scale Modes

Legend:

W = Whole step (2 semitones) | H = Half step (1 semitone)

Blackened rectangles = Notes that belong to that specific mode/scale

White rectangles = Notes NOT in that mode/scale

Major Scale Modes: All these modes use the same 7 notes from the major scale, but each mode starts from a different degree.

Melodic Minor Modes: All these modes use the same 7 notes from the melodic minor scale, but each mode starts from a different degree. These modes are essential in jazz and modern music.

Moving from Scales to Chords

Now that you understand how scales and modes are built from specific patterns of intervals, let’s see how chords emerge naturally from these same scales.

When you play a melody, you move through the scale step by step (C-D-E-F-G…). But when you play a chord, you stack notes in thirds — that is, you skip every other note (C-E-G-B). This creates harmony instead of melody.

Every scale degree can serve as the root of a chord. The quality of that chord (major, minor, dominant, half-diminished, etc.) depends entirely on the intervals available in the parent scale. This is why each mode produces its own unique palette of chords.

In the section below, you’ll see exactly which chords are built on each degree of every mode. Understanding this relationship between scales and chords is fundamental to jazz improvisation, composition, and understanding how harmony works in music.

Important: Change in Visual Representation

Above, we used 12 rectangles representing the 12 semitones (chromatic half-steps) to show which notes from the chromatic scale belong to each mode.

Below, we switch to using 10 boxes representing scale degrees (the 7 notes of each scale, extended to degree 10 for chord building). The numbers now represent positions within the 7-note scale, not chromatic half-steps.

Example in C Major:
• Semitones (above): 1=C, 2=C#, 3=D, 4=D#, 5=E, 6=F, 7=F#, 8=G, 9=G#, 10=A, 11=A#, 12=B
• Scale degrees (below): 1=C, 2=D, 3=E, 4=F, 5=G, 6=A, 7=B, 8=C, 9=D, 10=E

Building Seventh Chords on Each Scale Degree

Chord Legend:

Red highlighted boxes = The four notes that make up each seventh chord (root, 3rd, 5th, 7th)

Chord Symbols:

• maj7 = Major seventh (1-3-5-7)
• m7 or min7 = Minor seventh (1-♭3-5-♭7)
• 7 = Dominant seventh (1-3-5-♭7)
• m7♭5 = Half-diminished seventh (1-♭3-♭5-♭7)
• m(maj7) = Minor-major seventh (1-♭3-5-7)
• maj7#5 = Major seventh augmented fifth (1-3-#5-7)

Notice how each mode produces its own unique sequence of chord qualities. This is the foundation of jazz harmony and helps you understand which chords naturally fit together in different musical contexts. The extended grid to 10 degrees ensures that chords built on the 7th degree (like Bm7♭5 in C major, which needs notes B-D-F-A or degrees 7-9-11-13) can be shown completely.